Q: What is the condition for the addition of matrices?

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madhar chod

The usual rules of addition of fractions apply.

Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.

Yes, because otherwise addition and subtraction are not defined.

Matrix arithmetic

Matrices can't be "computed" as such; only operations like multiplication, transpose, addition, subtraction, etc., can be done. What can be computed are determinants. If you want to write a program that does operations such as these on matrices, I suggest using a two-dimensional array to store the values in the matrices, and use for-loops to iterate through the values.

Only square matrices have inverses.

Addition of two matrices is simply performed by iterating over all of the elements and adding elements with like indices together. A c code snippet... for (i=0; i<N; i++) for (j=0; j<M; j++) c[i][j] = a[i][j] + b[i][j];

Algebraic Properties of Matrix Operations. In this page, we give some general results about the three operations: addition, multiplication.

I assume since you're asking if 2x2 invertible matrices are a "subspace" that you are considering the set of all 2x2 matrices as a vector space (which it certainly is). In order for the set of 2x2 invertible matrices to be a subspace of the set of all 2x2 matrices, it must be closed under addition and scalar multiplication. A 2x2 matrix is invertible if and only if its determinant is nonzero. When multiplied by a scalar (let's call it c), the determinant of a 2x2 matrix will be multiplied by c^2 since the determinant is linear in each row (two rows -> two factors of c). If the determinant was nonzero to begin with c^2 times the determinant will be nonzero, so an invertible matrix multiplied by a scalar will remain invertible. Therefore the set of all 2x2 invertible matrices is closed under scalar multiplication. However, this set is not closed under addition. Consider the matrices {[1 0], [0 1]} and {[-1 0], [0 -1]}. Both are invertible (in this case, they are both their own inverses). However, their sum is {[0 0], [0 0]}, which is not invertible because its determinant is 0. In conclusion, the set of invertible 2x2 matrices is not a subspace of the set of all 2x2 matrices because it is not closed under addition.

how is matrices is applicable in our life?

Only square matrices have a determinant

The singular form of matrices is matrix.

You add matrices by adding their respective terms - e.g. the element in the first row and sixth column of the sum is the sum of the elements in the addends' first rows and sixth columns. Wikipedia has a nice example of matrix addition that I linked below.

In mathematics matrices are made up of arrays of elements.

There are no matrices in the question!

I do not. I f*cking hate matrices. I multiply sheep.

no

It would be no different. Matrix addition is Abelian or commutative. Matrix mutiplication is not.

Matrices were used to organize data.

Yes, similar matrices have the same eigenvalues.

I could be wrong but I do not believe that it is possible other than for the null matrix.

Matrices have a wider application in engineering. Many problems can be transformed in to simultaneous equation and their solution can easily be find with the help of matrices.

It depends on the type of matrices you want to know. There are different ways to do different types.

Which one of those matrices is more comfortable to sleep on?

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